A. (f + g)(x) = f(x) + g(x) = 4x - 5 + 3x + 9 = 7x + 4
B. f.g (x) = f(x) * g(x) = (4x - 5)*(3x + 9) = 12x^2 + 36x - 15x - 45
= 12x^2 + 21x - 45
C Replace the x in f(x) by g(x):-
= 4(3x + 9) - 5
= 12x + 36 - 5
= 12x + 31
First of all, let's recall the area of a triangle, knowing its base (b) and height (h):
The exercise is showing you that, if you inscribe a polynomial with more and more side, the area of the polynomial will approximate the area of the circle better and better (you can see youself that the polygon is "filling" the circle more and more as the number of sides increase).
Now, the second column tells you the area of each of the triangles the polygon is split into. So, we can see that the first polygon is split into 3 triangles, each of them having base 1.73 and height 0.5.
So, the area of each triangle is
There are three of these triangles, so the area of the whole polygon is
In the second case, you have six triangles, each with base 1 and height 0.87. So, the whole area is
Finally, in the last case you have 8 triangles, each with base 0.77 and height 0.92. So, the whole area is
Answer: Yes, y does vary directly with x.
Constant of variation = 1/4
The function rule is y = (1/4)x
=========================================================
Explanation:
Let's assume that y does vary directly with x.
If that's the case, then we have an equation in the form y = kx, where k is the constant of variation.
Solving for k gets us k = y/x
For each row, divide the y value over the x value
- row one: k = y/x = 14/56 = 0.25
- row two: k = y/x = 20/80 = 0.25
- row three: k = y/x = 22/88 = 0.25
Each row yields the value k = 0.25 and it fully confirms y does vary directly with x.
So y = kx becomes y = 0.25x as the function rule, which is equivalent to y = (1/4)x
Answer:
the number of silver medals won by Brazil is 14
Step-by-step explanation:
The computation of the number of silver medals won by Brazil is shown below:
Given that
Total number of gold and silver medal wons by Brazil was 35
And, the ratio of number of gold medals to the number of silver medals be 3 : 2
Based on the above information
The number of silver medals won would be
= 35 × 2 ÷ (3 + 2)
= 35 × 2 ÷ 5
= 14
hence, the number of silver medals won by Brazil is 14
6x
Step-by-step explanation:
1.2(4x-1)=8x-2=6x
